The Biostatistics and Modeling core will provide services to each of the proposed Projects. In Project 1, the statistical core will have responsibility for the analysis of the clinical studies where complex analysis models are proposed. Of special importance in this project will be the development of the dynamic linear model and analyses of the data from clinical trial. In Project 2, statistical consulting will primarily focus on a review of the analyses performed by the principal investigators and for the performance of any complex analyses, as needed. A similar role will be met for Project 3. The dynamic linear model method of analysis of data obtained from the continuous monitoring of patients in the Neurosurgical Intensive Care Unit will be developed in this Core. Reference analyses of data obtained during the clinical trial described in the Overview will be performed to generate prior distributions for use in subsequent models. The development of a time-varying discount parameter will be performed and tested using these data. Several alternative formulations of the model will also be tested. A comparison of performance these models will be performed using data collected during the first two years of this grant period. The model which provides the best characterization of change in jugular oxygen saturation an which is most highly correlated with the dynamic measures of autoregulation will then be used in the following three years to validate the model. Mathematical model of cerebral blood flow and gas transport dynamic will be performed in this Core. These models will initially focus on the rat cerebral blood flow, and will have direct application to project 3. Once a satisfactory model is obtained for the rat, similar models will be constructed to reflect the data obtained from human studies. These models will be refined against the data obtained in Project 1. Additionally, the data obtained in Project 2 will provide information for the modeling of the control of vascular resistance and capacitance.